2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/152022We derive a uniform bound for the total betti number of a closed manifold in terms of a Ricci curvature lower bound, a conjugate radius lower bound and a diameter upper bound. The result is based on an angle version of Toponogov comparison estimate for small triangles in a complete manifold with a Ricci curvature lower bound. We also give a uniform estimate on the generators of the fundamental group and prove a fibration theorem in this setting.18pages, LatexDifferential Geometrytext